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Title:  Convergence in Ergodic Theory 
Author(s):  Argiris, Georgios 
Doctoral Committee Chair(s):  Rosenblatt, Joseph 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics 
Abstract:  We investigate two problems involving convergence in ergodic theory. The first problem is the following: Given a measure preserving transformation T and a weight function w(alpha) → 0 as alpha → 0, is there a p > 0 such that the expression w(alpha)#{ n : 1n k=1nfT kx >a } have a limit, a.s. or in norm, as alpha → 0 for all functions f ∈ Lp0 [0,1]? No, we show. Here # denotes counting measure and f's are taken to be meanzero functions. We also consider similar questions for the more general operator w(alpha)#{n : 1nq k=1n f(Tk(x)) > alpha}, q > 1. The second problem addressed is to give arithmetic and probabilistic characterizations on the integer sequence ( nk) such that the series of ergodic differences k=1infinity ( Ank+1fAnkf ), where An denotes the usual ergodic averages, converges unconditionally for all functions f in some Lp space. 
Issue Date:  2001 
Type:  Text 
Language:  English 
Description:  51 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 2001. 
URI:  http://hdl.handle.net/2142/86781 
Other Identifier(s):  (MiAaPQ)AAI3023009 
Date Available in IDEALS:  20150928 
Date Deposited:  2001 
This item appears in the following Collection(s)

Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois